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Permanent fuzzy graphs with application in decision making
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DOI：10.1007/s00500-026-11414-8.png)
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Abstract
En 中文
In both classical graph theory and fuzzy graph theory, the number of nodes and arcs is conventionally considered fixed. As a result, removing one or more nodes from a graph usually results in a structure that cannot maintain its original function or may no longer be analyzed as the intended graph. To address this limitation, in this paper, we introduce, for the first time, a novel structure called the permanent graph (permanent fuzzy graph), utilizing the established concepts of neighborhood and distance between two nodes. By introducing this particular and useful graph structure, we propose a method to revive a graph whose functionality has been compromised due to the loss of nodes, thereby preventing its complete collapse. The application of this permanent graph (permanent fuzzy graph) in decision-making processes (specifically for making appropriate and informed choices within a social network) serves as evidence supporting this claim.
Keywords:
Graph
Fuzzy graph
Replaceable node
Decrease node
Increase arc
Permanent graph
Strong replaceable node
Strong decrease node
Strong increase node
Permanent fuzzy graph
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2.5
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2.1W
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Cited Papers